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Performance Analysis of Multi-processor Two-Stage Tandem Call Center Retrial Queues with Non-Reliable Processors Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2021-01-17 B. Krishna Kumar, R. Sankar, R. Navaneetha Krishnan, R. Rukmani
We analyze a multi-processor two-stage tandem call center retrial queueing network in which the processors are subject to active breakdowns and repairs at stage-I. A level-dependent quasi-birth-and-death (LDQBD) process is formulated and a sufficient condition for ergodicity of the system is discussed. Under the stability condition, the stationary distribution of the number of calls in the system,
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Batch Size Selection for Variance Estimators in MCMC Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2021-01-08 Ying Liu, Dootika Vats, James M. Flegal
We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error for this class of estimators. Further, we propose a parametric technique for estimating optimal batch sizes and discuss practical issues regarding the estimating process
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A New and Pragmatic Approach to the GI X /Geo/c/N Queues Using Roots Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-11-18 J. J. Kim, M. L. Chaudhry, V. Goswami, A. D. Banik
A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GIX/Geo/c/N is presented. In the past, various discrete-time queueing models, particularly the multi-server bulk-arrival queues with finite-buffer have been solved using complicated methods that lead to results in a non-explicit form. The purpose of this paper is to present a
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Variance Swaps Under Multiscale Stochastic Volatility of Volatility Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-11-16 Min-Ku Lee, See-Woo Kim, Jeong-Hoon Kim
Many hedge funds and retail investors demand volatility and variance derivatives in order to manage their exposure to volatility and volatility-of-volatility risk associated with their trading positions. The Heston model is a standard popular stochastic volatility model for pricing volatility and variance derivatives. However, it may fail to capture some important empirical features of the relevant
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Measuring Discrepancies Between Poisson and Exponential Hawkes Processes Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-11-13 Rachele Foschi
Poisson processes are widely used to model the occurrence of similar and independent events. However they turn out to be an inadequate tool to describe a sequence of (possibly differently) interacting events. Many phenomena can be modelled instead by Hawkes processes. In this paper we aim at quantifying how much a Hawkes process departs from a Poisson one with respect to different aspects, namely,
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Modelling Joint Behaviour of Asset Prices Using Stochastic Correlation Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-11-10 László Márkus, Ashish Kumar
Association or interdependence of two stock prices is analyzed, and selection criteria for a suitable model developed in the present paper. The association is generated by stochastic correlation, given by a stochastic differential equation (SDE), creating interdependent Wiener processes. These, in turn, drive the SDEs in the Heston model for stock prices. To choose from possible stochastic correlation
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Scan Statistics for Normal Data with Outliers Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-11-09 Qianzhu Wu, Joseph Glaz
In this article we investigate the performance of scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional normal data, in presence of outliers, when the population variance is unknown. For fixed window scan statistics, both the training sample and parametric bootstrap methods are employed for one and two dimensional normal
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An Evolutionary Model that Satisfies Detailed Balance Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-11-09 Jüri Lember, Chris Watkins
We propose a class of evolution models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and after that a genome is removed according to the selection scheme that involves fitness. Thus, the population size remains constant. The process evolves according to a Markov chain
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Correction to: Using Semi-Markov Chains to Solve Semi-Markov Processes Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-11-07 Bei Wu, Brenda Ivette Garcia Maya, Nikolaos Limnios
The original version of this article contained mistakes, and the author would like to correct them.
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On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-10-31 Nitis Mukhopadhyay
Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its
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Stochastic Modelling of Big Data in Finance Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-10-22 Anatoliy Swishchuk
We present a new approach to study big data in finance (specifically, in limit order books), based on stochastic modelling of price changes associated with high-frequency and algorithmic trading. We introduce a big data in finance, namely, limit order books (LOB), and describes them by Lobster data-academic data for studying LOB. Numerical results, associated with Lobster and other data, are presented
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Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-10-19 Srinivas R. Chakravarthy, Shruti, Alexander Rumyantsev
In this paper we consider a single server queueing model with under general bulk service rule with infinite upper bound on the batch size which we call group clearance. The arrivals occur according to a batch Markovian point process and the services are generally distributed. The customers arriving after the service initiation cannot enter the ongoing service. The service time is independent on the
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Small- t Expansion for the Hartman-Watson Distribution Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-10-09 Dan Pirjol
The Hartman-Watson distribution with density \(f_{r}(t)=\frac {1}{I_{0}(r)} \theta (r,t)\) with r > 0 is a probability distribution defined on \(t \in \mathbb {R}_{+}\), which appears in several problems of applied probability. The density of this distribution is given by an integral θ(r, t) which is difficult to evaluate numerically for small t → 0. Using saddle point methods, we obtain the first
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On the Rates of Asymptotic Normality for Bernstein Polynomial Estimators in a Triangular Array Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-10-06 Dawei Lu, Lina Wang
It is well known that the empirical distribution function has superior properties as an estimator of the underlying distribution function F. However, considering its jump discontinuities, the estimator is limited when F is continuous. Mixtures of the binomial probabilities relying on Bernstein polynomials lead to good approximation properties for the resulting estimator of F. In this paper, we establish
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An Unusual Application of Cramér-Rao Inequality to Prove the Attainable Lower Bound for a Ratio of Complicated Gamma Functions Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-10-02 Nitis Mukhopadhyay, Srawan Kumar Bishnoi
A specific function f(r) involving a ratio of complicated gamma functions depending upon a real variable r(> 0) is handled. Details are explained regarding how this function f(r) appeared naturally for our investigation with regard to its behavior when r belongs to R+. We determine explicitly where this function attains its unique minimum. In doing so, quite unexpectedly the customary Cramér-Rao inequality
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Queue-Length, Waiting-Time and Service Batch Size Analysis for the Discrete-Time GI/D-MSP (a,b) / 1 / ∞ $^{\text {(a,b)}}/1/\infty $ Queueing System Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-09-29 S. K. Samanta, R. Nandi
This paper analyzes an infinite-buffer single-server bulk-service queueing system in which customers arrive according to a discrete-time renewal process. The customers are served under the discrete-time Markovian service process according to the general bulk-service rule. The matrix-geometric method is used to obtain the queue-length distribution at prearrival epoch. The queue-length distributions
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Exact Results and Bounds for the Joint Tail and Moments of the Recurrence Times in a Renewal Process Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-09-29 Sotirios Losidis, Konstadinos Politis, Georgios Psarrakos
The best known result about the joint distribution of the backward and forward recurrence times in a renewal process concerns the asymptotic behavior for the tail of that bivariate distribution. In the present paper we study the joint behavior of the recurrence times at a fixed time point t, and we obtain both exact results and bounds for their joint tail behavior. We also obtain results about the
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Analysis of a Stochastic Competitive Model with Saturation Effect and Distributed Delay Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-09-26 Wenxu Ning, Zhijun Liu, Lianwen Wang, Ronghua Tan
This work is concerned with a novel stochastic competitive model with saturation effect and distributed delay, in which two coupling noise sources are incorporated and the interspecific competition delayed terms show saturation effect. A good understanding of exponential extinction, extinction, persistence in the mean and permanence in time average of two species are gained. Also, with the help of
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Using Semi-Markov Chains to Solve Semi-Markov Processes Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-09-15 Bei Wu, Brenda Ivette Garcia Maya, Nikolaos Limnios
This article provides a novel method to solve continuous-time semi-Markov processes by algorithms from discrete-time case, based on the fact that the Markov renewal function in discrete-time case is a finite series. Bounds of approximate errors due to discretization for the transition function matrix of the continuous-time semi-Markov process are investigated. This method is applied to a reliability
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Sequential Maximum Likelihood Estimation for the Squared Radial Ornstein-Uhlenbeck Process Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-09-09 Huantian Xie, Nenghui Kuang
In this paper, we study the properties of a sequential maximum likelihood estimator of the unknown parameter for the squared radial Ornstein-Uhlenbeck process. The estimator is proved to be closed, unbiased, normally distributed and strongly consistent. Lastly a simulation study is presented to illustrate the efficiency of the estimators.
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A New Class of Multivariate Elliptically Contoured Distributions with Inconsistency Property Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-09-03 Yeshunying Wang, Chuancun Yin
We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal distributions, conditional distributions, linear transformations, characteristic functions and dependence measure in the perspective of the inconsistency property. In
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Diffusion Approximation of Branching Processes in Semi-Markov Environment Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-08-22 Nikolaos Limnios, Elena Yarovaya
We consider continuous-time Markov branching processes in semi-Markov random environment and obtain diffusion approximation results for the near critical case. The problem of semi-Markov environment, presented here, is new and more interesting than the Markov case, since it includes many particular interesting cases: Markov, renewal, etc. The particular case of the Markov random environment of continuous-time
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Efficient Simulation of Ruin Probabilities When Claims are Mixtures of Heavy and Light Tails Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-27 Hansjörg Albrecher, Martin Bladt, Eleni Vatamidou
We consider the classical Cramér-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to efficiently simulate the ruin probability in this situation. The resulting estimators perform well for both small and large initial capital. We quantify the variance reduction
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Coupon Subset Collection Problem with Quotas Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-27 Shigeo Shioda
This paper studies the coupon subset collection problem with quotas, which is a variant of the classical coupon-collection problem. Specifically, the set of coupons is divided into distinct subsets, each of which is referred to as a class and each element of a class is referred to as a type. Coupons can be collected one by one by purchasing a coupon package. A coupon class is said to be acquired if
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Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials. Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-27 Spiros D Dafnis,Frosso S Makri,Markos V Koutras
In the present paper we study the distributions of families of patterns which generalize runs and patterns distributions extensively examined in the literature during the last decades. In our analysis we assume that the sequence of outcomes under investigation includes independent, but not necessarily identically distributed trials. An illustration is also provided how our new results could be exploited
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Sampling from Non-smooth Distributions Through Langevin Diffusion Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-17 Tung Duy Luu, Jalal Fadili, Christophe Chesneau
In this paper, we propose proximal splitting-type algorithms for sampling from distributions whose densities are not necessarily smooth nor log-concave. Our approach brings together tools from, on the one hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffusion equations, and in particular the Langevin diffusion. We establish in particular consistency guarantees
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Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-17 Moussa Kounta, Nathan J. Dawson
The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov regime switching. The optimal control problem is presented by making use of dynamic programming. In the case where the Markov chain has two states, the optimal homotopy analysis method (OHAM) is used to obtain an analytical approximation of the value function
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Bayesian Inference of a Parametric Random Spheroid from its Orthogonal Projections Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-13 Mathieu de Langlard, Fabrice Lamadie, Sophie Charton, Johan Debayle
The paper focuses on a new method for the inference of a parametric random spheroid from the observations of its 2D orthogonal projections. Such a stereological problem is well-known from the literature when the projections come from only one deterministic spheroid. Nevertheless, when the spheroid is random itself, the estimation of its distribution is not straightforward. From a theoretical viewpoint
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On Homogeneous Multivariate Distributions in Random Occupancy Models and Their Applications Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-10 Kiyoshi Inoue
In this article, we consider random occupancy models and the related problems based on the methods of generating functions. The waiting time distributions associated with sequential random occupancy models are investigated through the probability generating functions. We provide the effective computational tools for the evaluation of the probability functions by making use of the Bell polynomials.
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Privacy Considerations in Participatory Data Collection via Spatial Stackelberg Incentive Mechanisms Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-09 Jing Yang Koh, Gareth W. Peters, Ido Nevat, Derek Leong
Mobile crowd sensing is a widely used sensing paradigm allowing applications on mobile smart devices to routinely obtain spatially distributed data on a range of user attributes: location, temperature, video and audio. Such data then typically forms the input to application specific machine learning tasks to achieve objectives such as improving user experience, targeting geo-localised query based searches
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Truncated Family of Distributions with Applications to Time and Cost to Start a Business Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-02 Ayman Alzaatreh, Mohammad A. Aljarrah, Michael Smithson, Saman Hanif Shahbaz, Muhammad Qaiser Shahbaz, Felix Famoye, Carl Lee
The time and cost to start a business are highly related to the degree of transparency of business information, which strongly impacts the loss due to illicit financial flows. In order to study the distributional characteristics of time and cost to start a business, we introduce right-truncated and left-truncated T-X families of distributions. These families are used to construct new generalized families
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Statistical Estimation of Mutual Information for Mixed Model Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-07-01 Alexander Bulinski, Alexey Kozhevin
Asymptotic unbiasedness and L2-consistency are established for various statistical estimates of mutual information in the mixed models framework. Such models are important, e.g., for analysis of medical and biological data. The study of the conditional Shannon entropy as well as new results devoted to statistical estimation of the differential Shannon entropy are employed essentially. Theoretical results
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Asymptotic Results for the Absorption Time of Telegraph Processes with Elastic Boundary at the Origin Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-28 Claudio Macci, Barbara Martinucci, Enrica Pirozzi
We consider a telegraph process with elastic boundary at the origin studied recently in the literature (see e.g. Di Crescenzo et al. (Methodol Comput Appl Probab 20:333–352 2018)). It is a particular random motion with finite velocity which starts at x ≥ 0, and its dynamics is determined by upward and downward switching rates λ and μ, with λ > μ, and an absorption probability (at the origin) α ∈ (0
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Delayed Capital Injections for a Risk Process with Markovian Arrivals Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-21 A. S. Dibu, M. J. Jacob, Apostolos D. Papaioannou, Lewis Ramsden
In this paper we propose a generalisation to the Markov Arrival Process (MAP) risk model, by allowing for a delayed receipt of required capital injections whenever the surplus of an insurance firm is negative. Delayed capital injections often appear in practice due to the time taken for administrative and processing purposes of the funds from a third party or the shareholders of a firm. We introduce
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Upper and Lower Bounds for the Synchronizer Performance in Systems with Probabilistic Message Loss Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-20 Martin Zeiner, Ulrich Schmid
In this paper, we revisit the performance of the α-synchronizer in distributed systems with probabilistic message loss as introduced in Függer et al. [Perf. Eval. 93(2015)]. In sharp contrast to the infinite-state Markov chain resp. the exponential-size finite-state upper bound presented in the original paper, we introduce a polynomial-size finite-state Markov chain for a new synchronizer variant \(\alpha
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Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-19 Anatoliy Swishchuk
In this paper, we study so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit order books. We prove Law of Large Numbers (LLNs) and Functional Central Limit Theorems (FCLTs), the main results of the present paper, for both cases, non-regime-switching (Lemma 1 and Theorem 1) and regime-switching (Lemma 2 and Theorem 2) cases. The
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Generalized Evolutionary Point Processes: Model Specifications and Model Comparison Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-11 Philip A. White, Alan E. Gelfand
Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the history of the process. In this regard, we propose modeling which comprises generalization of the nonlinear Hawkes process. Working within a Bayesian framework, model fitting is implemented through Markov chain Monte Carlo. This entails discussion of computation
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Orderings of the Smallest Claim Amounts from Exponentiated Location-Scale Models Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-11 Sangita Das, Suchandan Kayal, N. Balakrishnan
In actuarial science, it is often of interest to compare stochastically extreme claim amounts from heterogeneous portfolios. In this regard, in the present work, we compare the smallest order statistics arising from two heterogeneous portfolios in the sense of the usual stochastic, hazard rate, reversed hazard rate and likelihood ratio orderings. We also consider the multiple-outlier model and obtain
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Extrinsic Regression and Anti-Regression on Projective Shape Manifolds Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-09 Vic Patrangenaru, Yifang Deng
Necessary and sufficient conditions for the existence of the extrinsic mean and extrinsic antimean of a random object (r.o.) X on a compact metric space \(\mathcal M,\) lead to considerations of extrinsic regression and antiregression functions on manifolds. One derives asymptotic distributions of kernel based estimators for antiregression functions with a numerical predictor, and use these in deriving
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q -Random Walks on Z d , d = 1, 2, 3 Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-08 Thomas Kamalakis, Malvina Vamvakari
In this work, we consider nearest neighbour q-random walks on Zd for d = 1,2,3, with transition probabilities q-varying by the number of steps, 0 < q < 1, and we study under which conditions these q-random walks are transient or recurrent. Also, we define the relative continuous time q-random walks on the integers and on the two dimensional integer lattices. Moreover, we present a q-Brownian motion
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Ornstein-Uhlenbeck Processes of Bounded Variation Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-06-01 Nikita Ratanov
Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion. There is an interval I such that the process starting from the internal point of I always remains within I. Starting outside, this process a. s. reaches this interval in a finite time. The distribution of the time for which
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Optimal Investment and Reinsurance Under the Gamma Process Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-05-26 Bohan Li, Junyi Guo
In this paper, the insurance company invests its wealth in a capital market composed of a riskless asset and a risky asset. The aggregate claim process of the insurance company is modeled by the Gamma process so as to make it closer to the reality. In practice, the insurance company provides not only those policies with large lose coverings but also policies with small ones. The Gamma process can describe
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Approximations for the Boundary Crossing Probabilities of Moving Sums of Random Variables Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-05-07 Jack Noonan, Anatoly Zhigljavsky
In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal random variables. We approximate a discrete time problem with a continuous time problem allowing us to apply established theory for stationary Gaussian processes. By then subsequently correcting approximations for discrete time, we show that the developed approximations are very accurate even
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The Periodic Solutions to a Stochastic Two-Prey One-Predator Population Model with Impulsive Perturbations in a Polluted Environment Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-05-06 Yuxiao Zhao, Linshan Wang, Yangfan Wang
In this paper, the periodic solutions of a stochastic two-prey one-predator model with impulsive perturbations in a polluted environment are focussed. The existence of global positive periodic solutions to the model are discussed by constructing the auxiliary system, and the sufficient conditions for the global attractivity of the periodic solutions are given by using Lyapunov method. An example is
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Stability and Instability of Steady States for a Branching Random Walk Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-05-04 Yaqin Feng, Stanislav Molchanov, Elena Yarovaya
We consider the time evolution of a lattice branching random walk with local perturbations. Under certain conditions, we prove the Carleman type estimation for the moments of a particle subpopulation number and show the existence of a steady state.
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On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo Methods Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-02-15 Marie Vialaret; Florian Maire
It is commonly admitted that non-reversible Markov chain Monte Carlo (MCMC) algorithms usually yield more accurate MCMC estimators than their reversible counterparts. In this note, we show that in addition to their variance reduction effect, some non-reversible MCMC algorithms have also the undesirable property to slow down the convergence of the Markov chain. This point, which has been overlooked
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On Exact and Asymptotic Formulas for the Distribution of the Integral of a Squared Brownian Motion with Drift Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-01-30 Weixuan Xia
The aim of this paper is to derive a set of easily implementable formulas regarding the probability distribution of the integral of a squared Brownian motion with drift. By reestablishing the characteristic function via the Karhunen-Loève transform, we obtain recurrence formulas for the moments as well as rapidly converging series with explicit coefficients for the probability density function and
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Weak Error for Nested Multilevel Monte Carlo Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-01-28 Daphné Giorgi; Vincent Lemaire; Gilles Pagès
This article discusses MLMC estimators with and without weights, applied to nested expectations of the form Ef(EF(Y,Z)|Y ). More precisely, we are interested on the assumptions needed to comply with the MLMC framework, depending on whether the payoff function f is smooth or not. A new result to our knowledge is given when f is not smooth in the development of the weak error at an order higher than
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A Renewal Generated Geometric Catastrophe Model with Discrete-Time Markovian Arrival Process Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-01-21 Nitin Kumar; U. C. Gupta
Any event that results in sudden change of the normal functioning of a system may be thought of as a catastrophe. Stochastic processes involving catastrophes have very rich application in modeling of a dynamic population in areas of ecology, marketing, queueing theory, etc. When the size of the population reduces abruptly as a whole, due to a catastrophe, it is termed as the total catastrophe. However
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On Estimation for Brownian Motion Governed by Telegraph Process with Multiple Off States Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-01-21 V. Pozdnyakov; L. M. Elbroch; C. Hu; T. Meyer; J. Yan
Brownian motion whose infinitesimal variance changes according to a three-state continuous-time Markov Chain is studied. This Markov Chain can be viewed as a telegraph process with one on state and two off states. We first derive the distribution of occupation time of the on state. Then the result is used to develop a likelihood estimation procedure when the stochastic process at hand is observed at
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A Stochastic Single Vehicle Routing Problem with a Predefined Sequence of Customers and Collection of Two Similar Materials Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-01-16 Epaminondas G. Kyriakidis, Theodosis D. Dimitrakos, Constantinos C. Karamatsoukis
We suppose that a vehicle visits N ordered customers in order to collect from them two similar but not identical materials. The actual quantity and the actual type of material that each customer possesses become known only when the vehicle arrives at the customer’s location. It is assumed that the vehicle has two compartments. We name these compartments, Compartment 1 and Compartment 2. It is assumed
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On the Individuals Chart with Supplementary Runs Rules under Serial Dependence Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-01-10 Jungtaek Oh; Christian H. Weiß
To improve the sensitivity of a Shewhart control chart, it is common among practitioners to use supplementary runs rules. The performance of such runs rules charts is studied in the presence of positive autocorrelation caused by a first-order discrete autoregressive process. This type of data-generating process allows to compute the chart’s run length properties exactly and efficiently, by utilizing
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Discrete-type Approximations for Non-Markovian Optimal Stopping Problems: Part II Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-01-08 Sérgio C. Bezerra; Alberto Ohashi; Francesco Russo; Francys de Souza
In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Leão et al. (??2019) and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartingale state processes such as functionals of path-dependent stochastic differential equations
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Purely Sequential and k-Stage Procedures for Estimating the Mean of an Inverse Gaussian Distribution Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2020-01-03 Ajit Chaturvedi; Sudeep R. Bapat; Neeraj Joshi
In the first part of this paper, we propose purely sequential and k-stage (k ≥ 3) procedures for estimation of the mean μ of an inverse Gaussian distribution having prescribed ‘proportional closeness’. The problem is constructed in such a manner that the boundedness of the expected loss is equivalent to the estimation of parameter with given ‘proportional closeness’. We obtain the associated second-order
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ECM Algorithm for Auto-Regressive Multivariate Skewed Variance Gamma Model with Unbounded Density Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2019-12-23 Thanakorn Nitithumbundit; Jennifer S. K. Chan
The multivariate skewed variance gamma (MSVG) distribution is useful in modelling data with high density around the location parameter along with moderate heavy-tailedness. However, the density can be unbounded for certain choices of shape parameter. We propose a modification to the expectation-conditional maximisation (ECM) algorithm to calculate the maximum likelihood estimate (MLE) by introducing
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Analysis of Tollbooth Systems with Two Tandem Skill-Based Servers and Two Vehicle Types Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2019-12-21 Baoxian Chang; Tao Jiang; Qingqing Ye; Xudong Chai; Liwei Liu
The existing tollbooth systems with multi-type vehicles in transportation literature typically assume the servers are either dedicated for each vehicle type or generic for all vehicle types. Conversely, in this paper, we focus on studying two similar systems both with skill-based servers, i.e., each tollbooth can handle a given subset of vehicle types. Meanwhile, we assume that vehicles queue together
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On Generalized Berman Constants Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2019-12-10 Chengxiu Ling; Hong Zhang
Considering the important role in Gaussian related extreme value topics, we evaluate the Berman constants involved in the study of the sojourn time of Gaussian processes, given by$$ \mathcal{B}_{\alpha}^{h}(x, E) = {\int}_{\mathbb{R}} e^{z} \mathbb{P} \left\{{{\int}_{E} \mathbb{I}\left( \sqrt2B_{\alpha}(t) - |t|^{\alpha} - h(t) - z>0 \right) \text{d} t \!>\! x}\right\} \text{d} z,\quad x\in[0, \text{mes}(E)]
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Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2019-12-05 Antonio Dalessandro; Gareth W. Peters
There is now an increasingly large number of proposed concordance measures available to capture, measure and quantify different notions of dependence in stochastic processes. However, evaluation of concordance measures to quantify such types of dependence for different copula models can be challenging. In this work, we propose a class of new methods that involves a highly accurate and computationally
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Branching Collision Processes with Immigration Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2019-12-04 Anyue Chen; Junping Li; Jing Zhang
We consider the regularity and ergodic properties of the Branching Collision Process with Immigration (BCIP) in this paper. We establish an easy checking sufficient condition under which the Feller minimal BCIP is honest. We provide some good conditions under which the Feller minimal BCIP is positive recurrent and then establish an analytic form of the generating function of the stationary distribution
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Parameter Estimation for Non-Stationary Fisher-Snedecor Diffusion Methodol. Comput. Appl. Probab. (IF 0.809) Pub Date : 2019-12-02 A. M. Kulik; N. N. Leonenko; I. Papić; N. Šuvak
The problem of parameter estimation for the non-stationary ergodic diffusion with Fisher-Snedecor invariant distribution, to be called Fisher-Snedecor diffusion, is considered. We propose generalized method of moments (GMM) estimator of unknown parameter, based on continuous-time observations, and prove its consistency and asymptotic normality. The explicit form of the asymptotic covariance matrix